# Analysis and Algebra on Differentiable Manifolds

## A Workbook for Students and Teachers

• Authors
• P. M. Gadea
• J. Muñoz Masqué
Book

## Table of contents

1. Front Matter
Pages i-xv
2. P. M. Gadea, J. Muñoz Masqué
Pages 1-73
3. P. M. Gadea, J. Muñoz Masqué
Pages 75-111
4. P. M. Gadea, J. Muñoz Masqué
Pages 113-128
5. P. M. Gadea, J. Muñoz Masqué
Pages 129-182
6. P. M. Gadea, J. Muñoz Masqué
Pages 183-232
7. P. M. Gadea, J. Muñoz Masqué
Pages 233-349
8. P. M. Gadea, J. Muñoz Masqué
Pages 351-375
9. P. M. Gadea, J. Muñoz Masqué
Pages 377-417
10. P. M. Gadea, J. Muñoz Masqué
Pages 439-439
11. Back Matter
Pages 419-438

## About this book

### Introduction

A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Hence, there arises the natural question—how to attain a deeper understanding? One well-known way to gain an understanding is through underpinning the d- nitions, theorems and constructions with hierarchies of examples, counterexamples and exercises. Their choice, construction and logical order is for any teacher in global analysis an interesting, important and fun creating task.

### Keywords

Riemannian geometry Tensor manifold

### Bibliographic information

• DOI https://doi.org/10.1007/978-90-481-3564-6
• Copyright Information Springer Netherlands 2001
• Publisher Name Springer, Dordrecht
• eBook Packages
• Print ISBN 978-90-481-3563-9
• Online ISBN 978-90-481-3564-6
• About this book